The source said Brown issued the apology with team captains "standing with him" and that the team "treated him like a family member" afterward.
On Wednesday, Brown initiated a discussion with Mayock midway through practice, resulting in the confrontation that had sparked the team's impasse with the player, according to a team source.
A Raiders source confirmed Brown was unhappy with the fine levied by the team and, seeing Mayock watching practice, walked over and initiated an exchange with the GM. The Raiders source confirmed information from another league source who said Brown called Mayock a "cracker" and unleashed a barrage of "cuss words" during the altercation.
The team source said Mayock tried to keep his cool and defuse the situation.
"[Mayock] was like, 'I'm cool, I understand your displeasure,'" the source said. "[Mayock] sort of just like ... just walked away because he saw it escalate."
The source stressed the confrontation escalated quickly, but it never appeared to be getting physical, and players, including linebacker Vontaze Burfict, attempted to separate Brown from the situation in order to calm him down.
That led to the team planning to suspend Brown, according to ESPN's Adam Schefter.
The source said it appeared Brown had read the letter about the fine -- which he posted on Instagram -- before practice and was angry to begin with.
"When he saw [Mayock], he was like, 'I can address it,'" the team source said.
The Raiders source said of Brown: "Nobody works as hard. Nobody loves the game as much, but [it] seems like there is something that is distracting him from his love that [he] can't control."
Mayock told reporters that Brown was not at the facility Thursday and would not be practicing. He did not confirm or deny that Brown will be suspended.
Coach Jon Gruden also wouldn't divulge any specifics, saying after practice Thursday that the Raiders would "have an official announcement later." Gruden was asked if he saw the alleged incident between Brown and Mayock.
"Like I said, I'm not going to get into all of this," Gruden said. "Obviously, [Brown] wasn't here today, and when we have some information for you, we'll give it to you. ... I've been talking about the same guy every day.
"... I'm emotional about it, I hope you understand why. I think a lot of this guy. I think Antonio is a great receiver, and deep down I think he's a really good guy. So, I'm frustrated, I'm not going to say anything more about it, hope it all works out. But I don't have anything official to say about anything else until I get all the facts, and that's what I'm going to do."
Brown was listed as a non-participant for Thursday's practice.
Brown's agent, Drew Rosenhaus, told ESPN's Get Up! that he continues to hope there is a solution to the situation.
"Right now I think his relationship with Coach Gruden is good, very good," Rosenhaus said Friday. "I'm not going to get into his relationship with Mike Mayock, but I will say that we're hopeful that that will be a good one, as well. It has been in the past; it can be in the future."
Rosenhaus added: "Listen, the NFL is a workplace. And in workplace environments, not everything is perfect. Antonio is a new player on this football team and we're trying to make it a very good relationship across the board. But what is very common in a new relationship is you try to get things in a good place. And it takes time."
Thursday night, Rosenhaus told ESPN's Rob Demovsky at Chicago's Soldier Field that he has been in contact with Raiders officials and that his client wants to play in the season opener Monday night.
"That's up to the Raiders," Rosenhaus said. "If it's up to us, he would like to play. But, ultimately, that's going to be their decision. He would like to honor his contract and fulfill his commitment to the Raiders. That's what we're trying to hammer out with the team right now."
In the letter, Mayock informed Brown that he was being fined $13,950 for missing a walk-through on Aug. 22, an unexcused absence. The letter also mentioned the team previously had fined Brown $40,000 for missing camp on Aug. 18 -- the day the GM issued his ultimatum to Brown, saying, "It's time for him to be all-in or all-out, OK?"
ESPN's Paul Gutierrez contributed to this report.
Woody: AB apologizing opens possibility of him playing Monday
Damien Woody sees the possibility of Antonio Brown playing on Monday night after apologizing to the Raiders.